Sequences & series worksheet with answers

Free printable Sequences & series worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 18·(1/2)ᵏ.

a = 18r = 1/2k₀ = 1
S =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 24·(2/3)ᵏ.

a = 24r = 2/3k₀ = 1
S =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 1/(k(k + 4)).

ak = 1/(k(k + 4))
S =
4.Medium
AΣ (−1)ᵏ/kk = 1 … ∞BΣ 3ᵏ/k³k = 1 … ∞CΣ 3/k³k = 1 … ∞DΣ 10ᵏ/k!k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (−1)ᵏ/kB: Σ 3ᵏ/k³C: Σ 3/k³D: Σ 10ᵏ/k!
  1. 1A: Σ (−1)ᵏ/k
  2. 2B: Σ 3ᵏ/k³
  3. 3C: Σ 3/k³
  4. 4D: Σ 10ᵏ/k!
5.Hard

f(x) = ln(1 + x) is approximated by its Maclaurin polynomial of degree 3 at x = 0.3. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 3! = 6 to find the largest possible error |R₃|.

f(x) = ln(1 + x)n = 3x = 0.3M = 6
|R₃| =
6.Hard

Recognise the series and find its sum: S = Σk=1∞ (−1)k+1·0.2ᵏ/k.

ak = (−1)k+1·0.2ᵏ/k
S =

Answer key

  1. 1. S = 18
  2. 2. S = 48
  3. 3. S = 0.5208
  4. 4. B: Σ 3ᵏ/k³
  5. 5. |R₃| = 0.002025
  6. 6. S = 0.1823

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